A Supercell Storm Simulation Using a Nonhydrostatic Cloud-Resolving Model Based on a Hybrid Isentropic-Sigma Vertical Coordinate

2013 ◽  
Vol 141 (4) ◽  
pp. 1204-1215 ◽  
Author(s):  
Michael D. Toy
Keyword(s):  
Mass Flux ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Implicit Time ◽  
Vertical Coordinate ◽  
Model Based ◽  
Supercell Storm ◽  
Coordinate Model ◽  
Isentropic Coordinates

Abstract A three-dimensional simulation of a supercell storm is performed with a nonhydrostatic model based on a hybrid isentropic-sigma vertical coordinate. The coordinate is a terrain-following, height-based coordinate near the surface that smoothly transitions to potential temperature with height. Using isentropic coordinates provides the advantage of having zero cross-coordinate vertical mass flux for adiabatic flow, which virtually eliminates the numerical error in the vertical transport. The model uses an adaptive grid algorithm by which the coordinate surfaces may deviate from their target isentropes to maintain a sufficiently smooth mesh, while allowing the turbulence and vertical motion associated with convection to develop. The storm simulated by the hybrid-coordinate model compares well with simulations by Eulerian-coordinate models, but with the key difference being that the cross-coordinate mass flux is significantly smaller in much of the domain with the hybrid-coordinate model. A semi-implicit time-differencing scheme for numerically stabilizing vertically propagating acoustic modes in isentropic coordinates is also presented in the paper.

Incorporating Condensational Heating into a Nonhydrostatic Atmospheric Model Based on a Hybrid Isentropic–Sigma Vertical Coordinate

2011 ◽  
Vol 139 (9) ◽  
pp. 2940-2954 ◽  
Author(s):  
Michael D. Toy
Keyword(s):  
Mass Flux ◽  
Deep Convection ◽  
Atmospheric Model ◽  
Atmospheric Models ◽  
Vertical Coordinate ◽  
Adiabatic Flow ◽  
Model Based ◽  
Terrain Following ◽  
Environmental Air ◽  
Isentropic Coordinates

Using isentropic coordinates in atmospheric models has the advantage of eliminating the cross-coordinate vertical mass flux for adiabatic flow, and virtually eliminating the associated numerical error in the vertical transport. This is a significant benefit since much of the flow in the atmosphere is approximately adiabatic. Nonadiabatic processes, such as condensational heating, result in a nonzero vertical velocity [Formula: see text] in isentropic coordinates. A method for incorporating condensational heating into a nonhydrostatic atmospheric model based on a hybrid isentropic–sigma vertical coordinate is presented. The model is tested with various 2D moist simulations and the results are compared with those using a traditional terrain-following, height-based sigma coordinate. With the hybrid coordinate, there are improvements in the representation of the developing cloud field in a mountain wave experiment. In a simulation of deep convection, the adaptive hybrid coordinate successfully simulates the turbulent nature of the convection, while maintaining the quasi-Lagrangian nature of the isentropic coordinate in the surrounding dry air. The vertical cross-coordinate mass flux is almost zero in the environmental air, as well as in the stratosphere above the convective tower.

Impacts of Assimilating Measurements of Different State Variables with a Simulated Supercell Storm and Three-Dimensional Variational Method

2013 ◽  
Vol 141 (8) ◽  
pp. 2759-2777 ◽  
Author(s):  
Guoqing Ge ◽  
Jidong Gao ◽  
Ming Xue
Keyword(s):  
Potential Temperature ◽  
Three Dimensional ◽  
Horizontal Wind ◽  
Cold Pool ◽  
State Variables ◽  
Wind Fields ◽  
Simulation Experiments ◽  
Supercell Storm ◽  
The Impact ◽  
Analysis Quality

Abstract This paper investigates the impacts of assimilating measurements of different state variables, which can be potentially available from various observational platforms, on the cycled analysis and short-range forecast of supercell thunderstorms by performing a set of observing system simulation experiments (OSSEs) using a storm-scale three-dimensional variational data assimilation (3DVAR) method. The control experiments assimilate measurements every 5 min for 90 min. It is found that the assimilation of horizontal wind can reconstruct the storm structure rather accurately. The assimilation of vertical velocity , potential temperature , or water vapor can partially rebuild the thermodynamic and precipitation fields but poorly retrieves the wind fields. The assimilation of rainwater mixing ratio can build up the precipitation fields together with a reasonable cold pool but is unable to properly recover the wind fields. Overall, data have the greatest impact, while have the second largest impact. The impact of is the smallest. The impact of assimilation frequency is examined by comparing results using 1-, 5-, or 10-min assimilation intervals. When is assimilated every 5 or 10 min, the analysis quality can be further improved by the incorporation of additional types of observations. When are assimilated every minute, the benefit from additional types of observations is negligible, except for . It is also found that for , , and measurements, more frequent assimilation leads to more accurate analyses. For and , a 1-min assimilation interval does not produce a better analysis than a 5-min interval.

scholarly journals Isentropic Analysis of Convective Motions

2013 ◽  
Vol 70 (11) ◽  
pp. 3673-3688 ◽  
Author(s):  
Olivier M. Pauluis ◽  
Agnieszka A. Mrowiec
Keyword(s):  
Mass Transport ◽  
Gravity Waves ◽  
Mass Flux ◽  
Potential Temperature ◽  
Three Dimensional ◽  
High Energy ◽  
Equivalent Potential Temperature ◽  
Equivalent Potential ◽  
Convective Motions ◽  
The Mean

Abstract This paper analyzes the convective mass transport by sorting air parcels in terms of their equivalent potential temperature to determine an isentropic streamfunction. By averaging the vertical mass flux at a constant value of the equivalent potential temperature, one can compute an isentropic mass transport that filters out reversible oscillatory motions such as gravity waves. This novel approach emphasizes the fact that the vertical energy and entropy transports by convection are due to the combination of ascending air parcels with high energy and entropy and subsiding air parcels with lower energy and entropy. Such conditional averaging can be extended to other dynamic and thermodynamic variables such as vertical velocity, temperature, or relative humidity to obtain a comprehensive description of convective motions. It is also shown how this approach can be used to determine the mean diabatic tendencies from the three-dimensional dynamic and thermodynamic fields. A two-stream approximation that partitions the isentropic circulation into a mean updraft and a mean downdraft is also introduced. This offers a straightforward way to identify the mean properties of rising and subsiding air parcels. The results from the two-stream approximation are compared with two other definitions of the cloud mass flux. It is argued that the isentropic analysis offers a robust definition of the convective mass transport that is not tainted by the need to arbitrarily distinguish between convection and its environment, and that separates the irreversible convective overturning from oscillations associated with gravity waves.

scholarly journals Design of a Nonhydrostatic Atmospheric Model Based on a Generalized Vertical Coordinate

2009 ◽  
Vol 137 (7) ◽  
pp. 2305-2330 ◽  
Author(s):  
Michael D. Toy ◽  
David A. Randall
Keyword(s):  
Atmospheric Model ◽  
Static Stability ◽  
Vertical Coordinate ◽  
Adiabatic Flow ◽  
Pressure Drag ◽  
Model Based ◽  
Ale Methods ◽  
Coordinate Model ◽  
Atmospheric Motion ◽  
Limiting Case

The isentropic system of equations has particular advantages in the numerical modeling of weather and climate. These include the elimination of the vertical velocity in adiabatic flow, which simplifies the motion to a two-dimensional problem and greatly reduces the numerical errors associated with vertical advection. The mechanism for the vertical transfer of horizontal momentum is simply the pressure drag acting on isentropic coordinate surfaces under frictionless, adiabatic conditions. In addition, vertical resolution is enhanced in regions of high static stability, which leads to better resolution of features such as the tropopause. Negative static stability and isentropic overturning frequently occur in finescale atmospheric motion. This presents a challenge to nonhydrostatic modeling with the isentropic vertical coordinate. This paper presents a new nonhydrostatic atmospheric model based on a generalized vertical coordinate. The coordinate is specified in a manner similar to that of Konor and Arakawa, but “arbitrary Eulerian–Lagrangian” (ALE) methods are used to maintain coordinate monotonicity in regions of negative static stability and to return the coordinate surfaces to their isentropic “targets” in statically stable regions. The model is mass conserving and implements a vertical differencing scheme that satisfies two additional integral constraints for the limiting case of z coordinates. The hybrid vertical coordinate model is tested with mountain-wave experiments including a downslope windstorm with breaking gravity waves. The results show that the advantages of the isentropic coordinate are realized in the model with regard to vertical tracer and momentum transport. Also, the isentropic overturning associated with the wave breaking is successfully handled by the coordinate formulation.

scholarly journals A Trajectory Mapping Technique for the Visualization and Analysis of Three-Dimensional Flow in Supercell Storms

2017 ◽  
Vol 34 (1) ◽  
pp. 33-49 ◽  
Author(s):  
Daniel P. Betten ◽  
Michael I. Biggerstaff ◽  
Louis J. Wicker
Keyword(s):  
Cloud Model ◽  
Flow Behavior ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Mapping Method ◽  
Mapping Technique ◽  
Complex Flow ◽  
Spatial And Temporal Scales ◽  
Trajectory Mapping

AbstractA visualization technique that allows simultaneous spatial analysis of complex flow behavior from thousands of Lagrangian trajectories is presented and tested using a high temporal and spatial resolution cloud model. The utility of the trajectory mapping technique is illustrated by showing that the source height of the air trajectories is a good proxy to the model-derived equivalent potential temperature. Moreover, the history of the forcing of vertical momentum is related to instantaneous vertical motion patterns shown to be elucidated in the trajectory mapping framework. The robustness of the trajectory mapping method was evaluated by integrating tendency terms and comparing Lagrangian-derived quantities to instantaneous values in the model. The original trajectory maps were also compared to those where the original fields have been filtered and/or the available data frequency are limited to the spatial and temporal scales typical of research radar datasets. The trajectory mapping method was applied to a supercell observed on 29 May 2004 to demonstrate that trajectory behavior for the observed case compares well to those from the higher-resolution numerical model output.

scholarly journals Simulations of column-average CO<sub>2</sub> and CH<sub>4</sub> using the NIES TM with a hybrid sigma-isentropic (σ−θ) vertical coordinate

2012 ◽  
Vol 12 (3) ◽  
pp. 8053-8106 ◽  
Author(s):  
D. A. Belikov ◽  
S. Maksyutov ◽  
V. Sherlock ◽  
S. Aoki ◽  
N. M. Deutscher ◽  
...  
Keyword(s):  
Transport Model ◽  
Three Dimensional ◽  
Model Performance ◽  
Vertical Motion ◽  
West Siberia ◽  
Total Carbon ◽  
Tracer Transport ◽  
Chemical Transport Model ◽  
Near Surface ◽  
Vertical Coordinate

Abstract. We have developed an improved version of the National Institute for Environmental Studies (NIES) three-dimensional chemical transport model (TM) designed for accurate tracer transport simulations in the stratosphere, given the use of a hybrid sigma-isentropic (σ−θ) vertical coordinate that employs both terrain following and isentropic parts switched smoothly around the tropopause. The air-ascending rate was derived from the effective heating rate and was used to simulate vertical motion in the isentropic part of the grid (above level 350 K), which was adjusted to fit to the observed age of the air in the stratosphere. Multi-annual simulations were conducted using NIES TM to evaluate vertical profiles and dry-air column-averaged mole fractions of CO2 and CH4. Comparisons with balloon-borne observations over Sanriku (Japan) in 2000–2007 revealed that the tracer transport simulations in the upper troposphere and lower stratosphere are performed with accuracies of ~5% for CH4 and SF6, and ~1% for CO2 compared with the observed volume-mixing ratios. The simulated XCO2 and XCH4 were evaluated against daily ground-based high-resolution Fourier Transform Spectrometer (FTS) observations measured at twelve sites of the Total Carbon Column Observing Network (TCCON) (Bialystok, Bremen, Darwin, Garmisch, Izaña, Lamont, Lauder, Orleans, Park Falls, Sodankylä, Tsukuba, and Wollongong) between January 2009 and January 2011. The comparison shows the model's ability to reproduce the site-dependent seasonal cycles as observed by TCCON, with correlation coefficients typically on the order 0.8–0.9 and 0.4–0.8 for XCO2 and XCH4, respectively, and mean model biases of ±0.2% and ±0.5%, excluding Sodankylä, where strong biases are found. The capturing of tracer total column mole fractions is strongly dependent on the model's ability to reproduce seasonal variations in tracer concentrations in the planetary boundary layer (PBL). We found a marked difference in the model's ability to reproduce near-surface concentrations at sites located some distance from multiple emission sources and where high emissions play a notable role in the tracer's budget. Comparisons with aircraft observations over Surgut (West Siberia), in an area with high emissions of methane from wetlands, show contrasting model performance in the PBL and in the free troposphere. This is another instance where the representation of the PBL is critical in simulating the tracer total columns.

scholarly journals DYNAMICO, an icosahedral hydrostatic dynamical core designed for consistency and versatility

2015 ◽  
Vol 8 (2) ◽  
pp. 1749-1800 ◽  
Author(s):  
T. Dubos ◽  
S. Dubey ◽  
M. Tort ◽  
R. Mittal ◽  
Y. Meurdesoif ◽  
...  
Keyword(s):  
Hamiltonian Structure ◽  
Potential Temperature ◽  
Time Integration ◽  
Hamiltonian Formulation ◽  
Three Dimensional ◽  
Primitive Equations ◽  
Finite Volume Scheme ◽  
Dynamical Core ◽  
Vertical Coordinate ◽  
Model Code

Abstract. The design of the icosahedral dynamical core DYNAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way. The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite volume scheme with slope limiting for positivity. Explicit Runge–Kutta time integration is used for dynamics and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately. Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.

scholarly journals DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility

2015 ◽  
Vol 8 (10) ◽  
pp. 3131-3150 ◽  
Author(s):  
T. Dubos ◽  
S. Dubey ◽  
M. Tort ◽  
R. Mittal ◽  
Y. Meurdesoif ◽  
...  
Keyword(s):  
Hamiltonian Structure ◽  
Potential Temperature ◽  
Time Integration ◽  
Hamiltonian Formulation ◽  
Three Dimensional ◽  
Primitive Equations ◽  
Finite Volume Scheme ◽  
Dynamical Core ◽  
Vertical Coordinate ◽  
Model Code

Abstract. The design of the icosahedral dynamical core DYNAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way. The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite-volume scheme with slope limiting for positivity. Explicit Runge–Kutta time integration is used for dynamics, and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately. Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.

scholarly journals Numerically Simulated Electrification and Lightning of the 29 June 2000 STEPS Supercell Storm

2006 ◽  
Vol 134 (10) ◽  
pp. 2734-2757 ◽  
Author(s):  
Kristin M. Kuhlman ◽  
Conrad L. Ziegler ◽  
Edward R. Mansell ◽  
Donald R. MacGorman ◽  
Jerry M. Straka
Keyword(s):  
Mass Flux ◽  
Cloud Model ◽  
Three Dimensional ◽  
Cloud Water ◽  
Severe Thunderstorm ◽  
Charge Structure ◽  
Flash Rate ◽  
Supercell Storm ◽  
Mapping Array ◽  
Cloud To Ground Lightning

Abstract A three-dimensional dynamic cloud model incorporating airflow dynamics, microphysics, and thunderstorm electrification mechanisms is used to simulate the first 3 h of the 29 June 2000 supercell from the Severe Thunderstorm Electrification and Precipitation Study (STEPS). The 29 June storm produced large flash rates, predominately positive cloud-to-ground lightning, large hail, and an F1 tornado. Four different simulations of the storm are made, each one using a different noninductive (NI) charging parameterization. The charge structure, and thus lightning polarity, of the simulated storm is sensitive to the treatment of cloud water dependence in the different NI charging schemes. The results from the simulations are compared with observations from STEPS, including balloon-borne electric field meter soundings and flash locations from the Lightning Mapping Array. For two of the parameterizations, the observed “inverted” tripolar charge structure is well approximated by the model. The polarity of the ground flashes is opposite that of the lowest charge region of the inverted tripole in both the observed storm and the simulations. Total flash rate is well correlated with graupel volume, updraft volume, and updraft mass flux. However, there is little correlation between total flash rate and maximum updraft speed. Based on the correlations found in both the observed and simulated storm, the total flash rate appears to be most representative of overall storm intensity.

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